This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060159 #32 Jan 05 2025 19:51:36 %S A060159 12,20,110,510,131052,12751220,10000095,2162049150,124324220,1, %T A060159 920067411130599,43494229746440272890, %U A060159 12100324200007455010742303399999999999999999990,4201420328711160916072939999999999999999999999999999999999999996 %N A060159 Initial term of a series of exactly n consecutive Harshad or Niven numbers (a Harshad number is such that is divided by the sum of its digits). %C A060159 Cooper and Kennedy (1993) proved that this sequence contains 20 terms. - _Sergio Pimentel_, Sep 18 2008 %C A060159 a(16) = 50757686696033684694106416498959861492*10^280 - 9 and a(17) = 14107593985876801556467795907102490773681*10^280 - 10. - _Max Alekseyev_, Apr 07 2013 %C A060159 H. G. Grundman (1994) extended the Cooper and Kennedy result to show that there are 2b but not 2b + 1 consecutive Harshad numbers in any base b. - _Jianing Song_, Dec 16 2024 %D A060159 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 110, p. 39, Ellipses, Paris 2008. %H A060159 C. N. Cooper and R. E. Kennedy, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/31-2/cooper.pdf">On consecutive Niven numbers</a>, Fibonacci Quart, (1993) 21, 146-151. %H A060159 H. G. Grundman, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/32-2/grundman.pdf">Sequences of consecutive n-Niven numbers</a>, Fibonacci Quarterly, (1994), 32 (2): 174-175. %H A060159 B. Wilson, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/35-2/wilson.pdf">Construction of 2n Consecutive n-Niven Numbers</a>, Fibonacci Quarterly, (1997), 35, 122-128. %H A060159 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_129.htm">Puzzle 129. Earliest sets of K consecutive Harshad Numbers</a>, The Prime Puzzles and Problems Connection. %H A060159 Wikipedia, <a href="https://en.wikipedia.org/wiki/Harshad_number">Harshad number</a> %e A060159 a(3) = 110 since (110, 111, 112) is the earliest run of 3 consecutive Harshad numbers: 110 is divisible by 1+1+0=2, 111 is divisible by 1+1+1=3, 112 is divisible by 1+1+2=4, but 109 is not divisible by 1+0+9=10, 113 is not divisible by 1+1+3=5, and there are no earlier runs of 3 consecutive numbers with this property. [Clarified by _Jianing Song_, Dec 16 2024] %Y A060159 Cf. A005349. %K A060159 fini,hard,nonn,base %O A060159 1,1 %A A060159 _Carlos Rivera_, Mar 12 2001 %E A060159 a(8) is found by _Jud McCranie_, Nov 13 2001 %E A060159 a(11)-a(13) are found by _Giovanni Resta_, Feb 21 2008 %E A060159 a(14), a(16)-a(17) from _Max Alekseyev_, Apr 07 2013